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Date May Example question Marks available 3 Reference code EXM.1.AHL.TZ0.35
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Hence and Find Question number 35 Adapted from N/A

Question

Write down the inverse of the matrix

A ( 1 3 1 2 2 1 1 5 3 )

[2]
a.

Hence, find the point of intersection of the three planes.

x 3 y + z = 1 2 x + 2 y z = 2 x 5 y + 3 z = 3

[3]
b.

A fourth plane with equation x + y + z = d  passes through the point of intersection. Find the value of d .

[1]
c.

Markscheme

A–1 = ( 0.1 0.4 0.1 0.7 0.2 0.3 1.2 0.2 0.8 )        A2  N2

[2 marks]

a.

For attempting to calculate ( x y z ) = A−1 ( 1 2 3 )       M1

x = 1.2 , y = 0.6 , z = 1.6  (so the point is (1.2, 0.6, 1.6))       A2   N2

[3 marks]

b.

(1.2, 0.6, 1.6) lies on  x + y + z = d

d = 3.4        A1   N1

[1 mark]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 1—Number and algebra » AHL 1.14—Introduction to matrices
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Topic 1—Number and algebra

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